Embedded Files
Chan, K. W. & Yau, C. Y. (2024). Asymptotically Constant Risk Estimator of the Time-average Variance Constant. Biometrika, 111, 825-842.
Abstract
Estimation of the time-average variance constant is important for statistical analyses involving dependent data. This problem is difficult as it relies on a bandwidth parameter. Specifically, the optimal choices of the bandwidths of all existing estimators depend on the estimand itself and another unknown parameter that is very difficult to estimate. Thus, optimal variance estimation is unachievable. In this paper, we introduce a concept of converging flat-top kernels for constructing variance estimators whose optimal bandwidths are free of unknown parameters asymptotically and hence can be computed easily. We prove that the new estimator has an asymptotically constant risk and is locally asymptotically minimax.
Journal official link: https://doi.org/10.1093/biomet/asae003
R code for a special case of the proposed estimator (converging Bartlett kernel):
lamTAVC = function(x, q=1){ n = length(x) xi = c(0.1518, 0.1912, 0.2070, 0.2154)[q] tau = c(0.2044, 0.2445, 0.2594, 0.2672)[q] phi = c(1.3228, 1.5929, 1.6599, 1.6771)[q] zeta = xi^tau l = min(max(ceiling(phi*n^(1/(1+2*q))), 2), n-1) l0 = ceiling(xi*l) w = rep(NA,l+1) w[1:(l0+1)] = rep(1-(zeta*l)^(-q),l0+1) k = (l0+1):(l) w[k+1] = 2*(1-(zeta*l)^(-q))/(1-xi)^3*((k/l)-1)^2*((k/l)-(3*xi-1)/2) acvf = c(acf(x,type="covariance",lag.max=l,plot=FALSE)$acf) w[1]*acvf[1]+2*sum(w[-1]*acvf[-1])}x = arima.sim(200, model=list(ar=.5,ma=.5))lamTAVC(x, q=1) # true value = 9
Google Sites
Report abuse